The present paper points out a novel scenario for the formation of chaotic attractors in a class of models of excitable cell membranes near an Andronov-Hopf bifurcation (AHB). The mechanism underlying chaotic dynamics admits a simple and visual description in terms of the families of one-dimensional first-return maps, which are constructed using the combination of asymptotic and numerical techn...

This paper deals with the problem of characterizing and stabilizing periodic orbits of a 1-DOF hopping robot moving over a nonlinear compliant surface. It is shown, through implicit calculations of the Poincare map, that globally stable periodic motions are possible via the injection of nonlinear damping.

An approximate Poincare map near equally strong multiple resonances is reduced by means the method of averaging. Near the resonance junction of three degrees of freedom, we find that some homoclinic orbits “whiskers” in single resonance lines survive and form nearly periodic orbits, each of which looks like a pair of homoclinic orbits.

in this paper, we prove that every metric line in the poincare ball model of hyperbolic geometry is exactly a classical line of itself. we also proved nonexistence of periodic lines in the poincare ball model of hyperbolic geometry.

Precise segmentation is a prerequisite for an accurate quantification of the imaged objects. It is a very challenging task in many medical imaging applications due to relatively poor image quality and data scarcity. In this work, we present an innovative segmentation paradigm, named Deep Poincaré Map (DPM), by coupling the dynamical system theory with a novel deep learning based approach. First...

Certain spaces satisfying Poincare duality are shown to have the homotopy type of simple Poincare complexes. The motivation for and applications of this result are the study of free actions of finite groups on manifolds. Let X be a finite CW complex with finite fundamental group ir. Then X is an n-dimensional Poincare complex if there is a class [X] E H, (X) such that the slant product with the...